FISHERY BULLETIN: VOL. 74, NO. 3 



situation appears. This may be conceptually 

 treated as though the diameters were under some 

 common influence, somewhat like iron filings in a 

 rectilinear magnetic field. Figure 3 shows such an 

 arrangement, where all diameters are in the first 

 case at an angle of 30° to a major axis and 15° in 

 the second case. Obviously the continuous lines of 

 the major axes of Figure 2 are no longer possible 

 except when the diameters are at one of the three 

 angles of the major axes, where in each case such a 

 drawing would show only a series of continuous 

 parallel lines. In any of these parallel arrange- 

 ments the distances of the diameters from end to 

 end are constant throughout as are the distances 

 from side to side. These two dimensions change 

 only if the angle between the diameters and major 

 axes is changed, as can be seen by comparing 

 Figures 4 and 5 based on a square with Figures 2, 

 3A, and 3B based on a hexagon. 



These two types of packing may now be con- 

 sidered in their more complex form in three 

 dimensional space. The cubic space lattice is very 

 simple and will be referred to later; the rhombic 

 spatial array, more likely to be confusing, is 



B 



Figure 3. -Parallel diameters drawn on the form of Figure 2. A. 

 Based on diameters halfway between two major axes, 30° from 

 either. B. Based on half the angular distance used in A, 15°. 



Figure 4.-Cubic packing of a single layer of spheres or circles, 

 directly comparable with Figure 2. 



Figure 5.- Parallel diameters drawn on the frame of Figure 4, 

 based on diameters halfway between two consecutive axes, 45° 

 from either. Directly comparable with Figure 3. 



discussed in sufficient detail for present needs. 

 Starting with the single layer of spheres of Figure 

 2, another layer may be placed upon it so that each 

 sphere of the second layer rests in the hollow 

 between three adjacent spheres of the first. The 

 second layer automatically has a pattern identical 

 to the first, but the centers of all the spheres of the 

 upper layer are displaced so as to fall over the 

 centers of an equilateral triangle connecting the 

 centers of the supporting first layer spheres. This 

 is shown in Figure 6 where the centers of the first 

 layer spheres are indicated by large circles and 

 those of the second by smaller dark circles. The 

 dash-line hexagon of Figure 6 indicates the dis- 

 placement of the second layer centers. It also 

 shows that just three second layer sphere centers 

 are within the solid-line hexagon. There are also 

 shown three similar small open circles forming a 

 similar pattern within the hexagon, which indicate 

 the absence of spheres centered by them, and 

 connected by dotted lines to form a hexagon of 

 absences. In the upper left corner of this same 



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